FIG. 1 shows a typical communication system 100 having a local/central unit 102 in communication with a remote unit 106 over a communication medium 104. Generally speaking, the communication medium 104 supports bi-directional communications between the local/central unit 102 and the remote unit 106. For convenience, communications from the local/central unit 102 to the remote unit 106 are said to be “downstream” communications, while communications from the remote unit 106 to the local/central unit 102 are said to be “upstream” communications. Thus, the communication medium 104 typically supports a downstream channel over which the local/central unit 102 communicates to the remote unit 106 and an upstream channel over which the remote unit 106 communicates to the local/central unit 102. The upstream channel and the downstream channel may share the same physical communication link or occupy different physical communication links. When the upstream channel and the downstream channel share the same physical communication link, the upstream channel and the downstream channel may occupy the same frequency band (e.g., analog modem channels) or different, typically non-overlapping, frequency bands (e.g., ADSL or cable modem channels). The upstream and downstream channels may be symmetric or asymmetric.
Within the communication system 100, it is common for the upstream and downstream communication channels to have dispersive characteristics. Specifically, each channel has a particular impulse response that disperses signals carried over the channel by extending the effects of each signal over a period of time. In many cases, the dispersive nature of the channel causes various distortions of the signals carried over the channel, such as Inter-Symbol Interference (ISI), Inter-Carrier Interference (ICI), and other distortions.
FIG. 2A shows a representation of an exemplary transmit signal 210 that is transmitted over a dispersive channel, for example, by the local/central unit 102. The exemplary transmit signal 210 includes two symbols, S1 (211) and S2 (212), that are transmitted over the dispersive channel with no inter-symbol delay.
FIG. 2B shows a representation of an exemplary receive signal 220 that is received over the dispersive channel, for example, by the remote unit 106, when the symbols S1 (211) and S2 (212) are transmitted over the dispersive channel with no inter-symbol delay. As shown in FIG. 2B, the transmitted symbol S1 (211) is dispersed by the dispersive channel such that the received symbol R1 (221) overlaps the beginning of the symbol S2 (212). This causes ISI between the symbols S1 (211) and S2 (212) and therefore corruption of the symbol S2 (212).
One way to avoid or reduce ISI is to add a sufficient amount of inter-symbol delay to the transmitted symbols so that the received symbols do not overlap.
FIG. 3A shows a representation of an exemplary transmit signal 310 that is transmitted over a dispersive channel, for example, by the local/central unit 102. The exemplary transmit signal 310 includes two symbols, S1 (311) and S2 (312), that are transmitted over the dispersive channel with inter-symbol delay.
FIG. 3B shows a representation of an exemplary receive signal 320 that is received over the dispersive channel, for example, by the remote unit 106, when the symbols S1 (311) and S2 (312) are transmitted over the dispersive channel with inter-symbol delay. As shown in FIG. 3B, the transmitted symbols S1 (311) and S2 (312) are dispersed by the dispersive channel. However, because of the inter-symbol delay in the transmitted signal, the received symbols R1 (321) and R2 (322) do not overlap. As a result, there is no ISI between the symbols S1 (311) and S2 (312).
While the inter-symbol delay added to the transmitted signal eliminates (or at least reduces) ISI, there are detriments to employing such inter-symbol delay. For one, the inter-symbol delay reduces the efficiency of the transmitted signal in that fewer symbols (and therefore less data) are transmitted over a particular period of time. Also, the inter-symbol delay can cause cross-talk between channels carried over a common physical communication link. Thus, inter-symbol delay may be impractical for certain applications.
Another way to avoid or reduce ISI is to “shorten” the impulse response of the channel. This is typically done using a time-domain equalizer (TEQ) at the receiving end of the communication channel. The TEQ is a short Finite Impulse Response (FIR) filter that is used to time-compress (shorten) the impulse response of the communication channel. In addition to shortening the impulse response of the channel, the TEQ also tends to “flatten” the channel and amplify noise. The effectiveness of the TEQ has a direct impact on overall performance, and therefore the TEQ design and the TEQ coefficients must be carefully determined. There are typically different design considerations for time-domain equalization of the upstream and downstream channels. Also, whether the implementation platform is memory or processing power limited (or both) plays an important role in the TEQ design.
The following references are hereby incorporated herein by reference in their entireties, and may be referenced throughout the specification using the corresponding reference number. It should be noted that the reference numbers are not consecutive.    [1] John A. C. Bingham, ADSL, VDSL and Multicarrier Modulation, John Wiley & Sons, 2000.    [2]J. S. Chow, J. M. Cioffi, and J. A. C. Bingham “Equalizer Training Algorithms for Multicarrier Modulation Systems,” ICC 1993, May 1993, pp. 761–765.    [3] D. D. Falconer and F. R. Magee, Jr., “Adaptive Channel Memory Truncation for maximum Likelihood Sequence Estimator,” B.S.T.J. November 1973, pp. 1541–1562.    [5] D. T. Lee, B. Friedlander, and M. Morf, “Recursive Ladder Algorithms for ARMA Modeling,” IEEE Trans. Automat. Contr., vol. AC-27, No. 4, August 1982.    [6] P. J. W. Melsa, R. C. Younce, C. E. Rohrs, “Impulse Response Shortening for Discrete Multitone Transceivers,” IEEE Trans. Commun., vol. 44, No. 12, pp. 1662–1672, December 1996.    [7] N. Al-Dhahir, A. H. Sayed, and J. M. Cioffi, “Stable pole-zero modeling of long FIR filters with application to the MMSE-DFE,” IEEE Trans. Commun., vol. 45, No. 5, pp. 508–513, 1997.    [8] N. Al-Dhahir, A. H. Sayed, and J. M. Cioffi, “A high-performance cost-effective pole-zero MMSE-DFE,” Proc. Allerton Conf. Commun., Contr., Computing, September 1993, pp. 1166–1175.    [10] Steven M. Kay, Modern Spectral Estimation: Theory and Application, Prentice Hall, 1988.    [11] Peter E. Caines, Linear Stochastic Systems, John Wiley & Sons, 1988.    [13] N. Al-Dhahir and J. M. Cioffi, “A low complexity pole-zero MMSE Equalizer for ML Receivers,” Proc. Allerton Conf. Commun., Control, Comput., pp. 623–632, 1994.